Interactions of Discrete States with Nonzero Ghost Number \\ in $c=1$ $2D$ Gravity

TL;DR

This paper investigates the interactions of discrete states with nonzero ghost number in $c=1$ 2D quantum gravity, revealing a structure akin to area-preserving diffeomorphisms and suggesting a BRST-like symmetry in the system.

Contribution

It demonstrates that the interactions of these states are governed by the structure constants of area-preserving diffeomorphisms and derives the effective action, indicating a BRST-like symmetry.

Findings

Interactions follow the structure constants of area-preserving diffeomorphisms.

Effective action for the states is explicitly derived.

System exhibits a BRST-like symmetry.

Abstract

We study the interactions of the discrete states with nonzero ghost number in $c=1$ two-dimensional ($2D$) quantum gravity. By using the vertex operator representations, it is shown that their interactions are given by the structure constants of the group of the area preserving diffeomorphism similar to those of vanishing ghost number. The effective action for these states is also worked out. The result suggests the whole system has a BRST-like symmetry.